On the Factoriality of q-Deformed Araki-Woods von Neumann Algebras
The q-deformed Araki-Woods von Neumann algebras Γ q ( H R , U t ) ″ \documentclass[12pt]{minimal}
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\begin{document}$$\Gamma _q({\mathcal {H}}_{\mathbb {R}},U_t)^{\prime \prime }$$\end{document}
are factors for all q ∈ ( - 1 , 1 ) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym}
\usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} …
\usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}
\usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}
\begin{document}$$\Gamma _q({\mathcal {H}}_{\mathbb {R}},U_t)^{\prime \prime }$$\end{document}
are factors for all q ∈ ( - 1 , 1 ) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym}
\usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} …
Abstract
The q-deformed Araki-Woods von Neumann algebras \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Gamma _q({\mathcal {H}}_{\mathbb {R}},U_t)^{\prime \prime }$$\end{document} are factors for all whenever dim. When dim they are factors as well for all q so long as the parameter defining is ‘small’ or 1 (trivial) as the case may be.
Springer
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